Ratio, Proportion, Indices, LogarithmMCQMTP Dec 2023 Series IIQuestion 861 of 302
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If x/2=y/3=z/7\displaystyle x/2 = y/3 = z/7, then the value of (2x−5y+4z)/2y\displaystyle (2x-5y+4z)/2y is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option d — $17/6$

All Options:

  • A6/23\displaystyle 6/23
  • B$23/6$
  • C3/2\displaystyle 3/2
  • D$17/6$

Detailed Solution & Explanation

Given that:
x2=y3=z7x2=y3=z7\displaystyle \frac{x}{2} = \frac{y}{3} = \frac{z}{7}
Let us set these equal ratios to a common constant k\displaystyle k:
x2=y3=z7=kx2=y3=z7=k\displaystyle \frac{x}{2} = \frac{y}{3} = \frac{z}{7} = k
This gives the values of $x, y, z$ in terms of k\displaystyle k:
x=2k,y=3k,z=7kx = 2k, \quad y = 3k, \quad z = 7k
We want to evaluate the expression:
2x−5y+4z2y2x−5y+4z2y\displaystyle \frac{2x - 5y + 4z}{2y}
Substitute the values of x,y,\displaystyle x, y, and z\displaystyle z into the expression:
2(2k)−5(3k)+4(7k)2(3k)2(2k)−5(3k)+4(7k)2(3k)\displaystyle \frac{2(2k) - 5(3k) + 4(7k)}{2(3k)}
Simplify the terms in the numerator and the denominator:
Numerator=4k−15k+28k=(4−15+28)k=17kNumerator=4k−15k+28k\displaystyle \text{Numerator} = 4k - 15k + 28k = (4 - 15 + 28)k = 17k
Denominator=6kDenominator=6k\displaystyle \text{Denominator} = 6k
Now, divide the numerator by the denominator:
17k6k=17617k6k=176\displaystyle \frac{17k}{6k} = \frac{17}{6}
This matches **Option D**.
Hence, **Option D** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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